Fractional calculus, whose applications can be found in many disciplines including economics, life and physical sciences, as well as engineering, can be considered as one of the modern branches of mathematics [1]}, [2]}, [3]}, [4]}. Many problems of interests from these fields can be analyzed through fractional integrals, which can also be regarded as an interesting sub-discipline of fractional calculus. Some of the applications of integral calculus can be seen in the following papers [5,6,7,8,9,10], through which problems in physics, chemistry, and population dynamics were studied. The fractional integrals were extended to include the H–H inequality [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}. Now, we recall some basic definitions of fractional integrals as follows
